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Anton [14]
3 years ago
9

A map is drawn using a scale of 1 inch : 165 miles. The length of the road on the map is 12 inches. Find the actual length of th

e road.
Mathematics
1 answer:
maw [93]3 years ago
7 0

Answer:

x= 1980 miles

Step-by-step explanation:

1 inch is to 165 miles as 12 inches is to x

1/165=12/x

x=12*(165/1)

x= 1980

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What was the purpose of the coordinate graphing system described by Descartes in his book Discourse on Method?
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Find an equation for the line that passes through the points (5.-5) and (-4,-2)
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Answer:

\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept</em>

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (5, -5) and (-4, -2).

Substiute:

m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}

Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:

-5=-\dfrac{1}{3}(5)+b

-5=-\dfrac{5}{3}+b               <em>add 5/3 to both sides</em>

-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}

Finally we have the equation of a line in the slope-intercept form:

y=-\dfrac{1}{3}x-\dfrac{10}{3}

Convert to the standard form <em>(Ax + By = C)</em>:

y=-\dfrac{1}{3}x-\dfrac{10}{3}          <em>multiply both sides by 3</em>

3y=-x-10              <em>add x to both sides</em>

x+3y=-10

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3 years ago
The number of mosquitoes at the beach has increased by 50% every year since 2012. In 2012, there were 2,500 mosquitoes. How many
xxTIMURxx [149]

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Step-by-step explanation:

2012 = 2500

2500 x .50 = 1250

2500 + 1250

2013 = 3750

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5625 + 2812.5

2015= 8437.5

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2016= 12656.25

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12656.25 + 6328.125

2017= 18984.375

18984.375 x .50 = 9492.1875

18984.375 + 9492.1875

2018= 28,476.5625‬

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3 years ago
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